AI 中文总结
本研究在最小 seesaw 框架下，探讨辐射修正导致 μ-τ 反射对称性破缺，推导低能中微子参数与高能对应量的关系，数值分析表明偏离程度随 tanβ 增大而增加，结果符合实验约束。
AI 中文摘要
μ-τ 反射对称性预言了最大大气混合角 θ₂₃=π/4，以及狄拉克 CP 相位 δ=π/2 或 3π/2。近期全局分析表明这些预言存在微小但显著的偏离，说明该对称性是近似的，需要被破缺。受此启发，我们在最小 seesaw 框架下研究由辐射修正诱导的 μ-τ 反射对称性破缺，假设该对称性在高能 seesaw 标度 Λ_{μτ}=10¹⁴ GeV 处严格成立。最小 seesaw 的一个显著特征是存在一个无质量的轻中微子，仅保留一个物理马约拉纳 CP 相位。我们从有效马约拉纳中微子质量矩阵的单圈重整化群方程（RGE）积分解出发，推导了 Λ_{EW}=172.76 GeV 处低能中微子参数关于其高能对应量的解析表达式。随后我们在最小超对称标准模型（MSSM）中对低能参数进行数值估算，取 Λ_s=1 TeV，tanβ 分别为 10、30 和 50。我们分别对正常序（NO）和倒序（IO）两种情况进行分析，发现两种情况下预言的中微子质量和混合参数均与当前实验数据一致；中微子质量总和、雅尔斯科夫不变量 J 以及有效马约拉纳质量 |⟨m⟩_{ee}| 也满足当前实验约束。最后我们估算了低能中微子参数相对于其高能值的偏离程度，并研究其对 tanβ 的依赖关系，结果表明对于 NO 和 IO 两种情况，这些偏离的幅度均随 tanβ 的增大而增加。
英文摘要
The $μ$-$τ$ reflection symmetry predicts a maximal atmospheric mixing angle, $θ_{23}=π/4$, and Dirac CP phase, $δ=π/2$ or $3π/2$. Recent global analyses indicate small but significant deviations from these predictions, suggesting that the symmetry is approximate and requires breaking. Motivated by this, we study the breaking of $μ$-$τ$ reflection symmetry induced by radiative corrections in the minimal seesaw framework, assuming the symmetry to be exact at the high-energy seesaw scale $Λ_{μτ}=10^{14}~\mathrm{GeV}$. A distinctive feature of the minimal seesaw is that one light neutrino remains massless, leaving only one physical Majorana CP phase. Starting from the integral solution of the one-loop RGE for the effective Majorana neutrino mass matrix, we derive analytical expressions for the low-energy neutrino parameters at $Λ_{\mathrm{EW}}=172.76~\mathrm{GeV}$ in terms of their high-energy counterparts. We then numerically estimate the low-energy parameters within the MSSM, taking $Λ_s=1~\mathrm{TeV}$ and $\tanβ=10$, $30$ and $50$. The analysis is performed separately for Normal Order (NO) and Inverted Order (IO). We find that the predicted neutrino masses and mixing parameters are consistent with current experimental data in both scenarios. The sum of neutrino masses, Jarlskog invariant $J$, and effective Majorana mass $|\langle m\rangle_{ee}|$ also satisfy current experimental constraints. Finally, we estimate the amount of deviations of the low-energy neutrino parameters from their high-energy values and investigate their dependence on $\tanβ$. We find that the magnitude of these deviations increases with increasing $\tanβ$ for both NO and IO.
Comments30 pages, 24 figures
